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Majorized correspondences and equilibrium existence in discontinuous games

Author

Listed:
  • Pavlo Prokopovych

    (Kyiv School of Economics and Kyiv Economics Institute)

Abstract

This paper is aimed at widening the scope of applications of majorized correspondences. A new class of majorized correspondences -- domain U-majorized correspondences -- is introduced. For them, a maximal element existence theorem is established. Then, sufficient conditions for the existence of an equilibrium in qualitative games are provided. They are used to show the existence of a pure strategy Nash equilibrium in compact quasiconcave games that are either correspondence secure or correspondence transfer continuous.

Suggested Citation

  • Pavlo Prokopovych, 2014. "Majorized correspondences and equilibrium existence in discontinuous games," Discussion Papers 53, Kyiv School of Economics.
    • Handle: RePEc:kse:dpaper:53
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    File URL: http://repec.kse.org.ua/pdf/KSE_dp53.pdf
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    Cited by:

    1. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    2. Vincenzo Scalzo, 2018. "Weak maximal elements and weak equilibria in ordinal games with applications to exchange economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 29-39, April.
    3. M. Ali Khan & Richard P. McLean & Metin Uyanik, 2025. "Excess demand approach with non-convexity and discontinuity: a generalization of the Gale–Nikaido–Kuhn–Debreu lemma," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(4), pages 1167-1190, June.
    4. He, Wei & Yannelis, Nicholas C., 2015. "Discontinuous games with asymmetric information: An extension of Reny's existence theorem," Games and Economic Behavior, Elsevier, vol. 91(C), pages 26-35.
    5. Yang, Zhe & Yuan, George Xianzhi, 2019. "Some generalizations of Zhao’s theorem: Hybrid solutions and weak hybrid solutions for games with nonordered preferences," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 94-100.
    6. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    7. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.
    8. Wei He & Nicholas C. Yannelis, 2017. "A remark on discontinuous games with asymmetric information and ambiguity," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 119-126, April.
    9. Bhowmik, Anuj & Yannelis, Nicholas C., 2024. "Equilibria in abstract economies with a continuum of agents with discontinuous and non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 115(C).

    More about this item

    Keywords

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    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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